A wire having length l carries a current i directed along the x -axis. A magnetic field is present and is described by B = B₀ ( i + j + k ) T . Determine the magnitude of the magnetic force acting on the wire.

Step-by-step solution

The magnetic force acting on a current-carrying wire is given by F = i( l B ) . Since the wire is directed along the x -axis, the length vector is l = l i . The magnetic field is given as B = B₀ ( i + j + k ) . Substituting these into the force formula: F = i (l i B₀ ( i + j + k )) F = i l B₀ ( i i + i j + i k ) Using the properties of cross products, i i = 0 , i j = k , and i k = - j , we get: F = i l B₀ ( k - j ) The magnitude of the magnetic force is: | F | = i l B₀ (-1)^2 + (1)^2 = 2 B₀ i l